Optimal Average Satisfaction and Extended Justified Representation in Polynomial Time

TL;DR

This paper introduces a polynomial-time approval-based committee selection rule that achieves extended justified representation by approximately maximizing the PAV score through local search, ensuring high satisfaction for cohesive voter groups.

Contribution

It presents a new efficient algorithm for approval-based committee selection that guarantees extended justified representation and high voter satisfaction.

Findings

The rule admits a polynomial-time algorithm.

It provides almost optimal average satisfaction for cohesive groups.

High satisfaction implies extended justified representation.

Abstract

In this short note, we describe an approval-based committee selection rule that admits a polynomial-time algorithm and satisfies the Extended Justified Representation (EJR) axiom. This rule is based on approximately maximizing the PAV score, by means of local search. Our proof strategy is to show that this rule provides almost optimal average satisfaction to all cohesive groups of voters, and that high average satisfaction for cohesive groups implies extended justified representation.